Fourier transform, operator interpolation and Sobolev spaces; Regularization properties of solutions to the linear problem; Non-linear Schrödinger equation, local and global theory for the associated initial value problem; Generalized Korteweg-de Vries equation, local and global theory for the associated initial value problem; Generalizations.

Reference:
 LINARES, F., PONCE, G. – Introduction to nonlinear dispersive equations. Mathematical Publications, IMPA 2004.

* Basic syllabus. The professor has the autonomy to make any changes.